Detection and correction of phase jumps in a phase sequence

ABSTRACT

The invention relates to any receiver for MPSK (M=2 n ) modulation, in which an error correction device is used for correcting Tretter type frequency errors and, upstream of this device, a phase estimation device based on decisions made on the received symbols.  
     When the frequency error is such that, based on a certain symbol, an error is made in the decision, this error is translated by a phase jump of  
       ±     π     2     n   -   1                       
 
     in the sequence of phase estimations obtained. The frequency estimation obtained is then inaccurate.  
     A receiver according to the invention comprises means for calculating a phase sequence, called initial sequence, based on decisions made on symbols, and means for detecting and correcting phase jumps in this initial sequence, so as to supply a phase sequence, called final sequence, to said frequency error estimation means.  
     Applications: Interactive data transmission system—network head-ends.

FIELD OF THE INVENTION

[0001] The invention relates to a communication system comprising atleast a transmitter and a receiver intended to receive symbols comingfrom a PSK modulation, and comprising estimation means for estimating afrequency error relating to a symbol based on a sequence of symbolphases. The invention also relates to a receiver intended to be used insuch a communication system.

[0002] The invention also relates to a method of estimating a frequencyerror relating to a received symbol, coming from a PSK modulation, basedon a sequence of symbol phases, and to a method of detecting andcorrecting phase jumps in an initial phase sequence of symbols comingfrom a PSK modulation.

[0003] The invention finally relates to computer programs comprisinginstructions for implementing such methods.

BACKGROUND OF THE INVENTION

[0004] Such an estimation algorithm of a frequency error relating to areceived symbol based on a phase sequence is described, for example, inparagraph 4.1 (page 107) of the article <<Feedforward FrequencyEstimation for PSK: a Tutorial Review>>by M. Morelli and U. Mengali,published in the journal <<European Transactions on Telecommunications,vol. 9, no. 2, March-April 1998>>. This algorithm is known by the nameof Tretter algorithm, or least squares method.

[0005] To obtain such a phase sequence, it is known that a phaseestimation algorithm is used, which estimates the phase relating to areceived symbol on the basis of decisions made on various receivedsymbols. For example, the expectation maximization algorithm is used,which is described in paragraph 3.3 of the conference report of the<<International Conference on Communications, New Orleans, USA, 1-5 May,1994, vol. 2, pp. 940 and 945>>, entitled <<Comparison between digitalrecovery techniques in the presence of frequency shift>>by F. Daffaraand J. Lamour.

[0006] The problem posed is the following: in a PSK modulationcomprising 2^(n)points, two adjacent points have a phase difference of$\frac{\pi}{2^{n - 1}}.$

[0007] When the frequency error is such that, based on a certain symbol,an error is made in the decision, this error is translated by a phasejump of $\pm \frac{\pi}{2^{n - 1}}$

[0008] in the sequence of phase estimates obtained. The number of phasejumps that may be obtained depends on the number of symbols contained inthe packet and the initial frequency difference.

[0009] When the sequence of phases, which are used for applying theTretter algorithm, includes one or various phase jumps, the frequencyestimate obtained is inaccurate. The invention notably has for itsobject to provide a solution to this problem.

SUMMARY OF THE INVENTION

[0010] For this purpose, a communication system according to theinvention and as described in the opening paragraph is characterized inthat said receiver comprises calculation means for calculating a phasesequence, called initial sequence, based on decisions made on symbols,and means for detecting and correcting phase jumps in this initialsequence, to supply a phase sequence, called final sequence, to saidfrequency error estimation means.

[0011] Advantageously, said means for detecting and correcting phasejumps comprise:

[0012] —modifying means for modifying said initial sequence, so as toproduce a plurality of modified sequences which each compensate for aphase jump configuration,

[0013] —calculation means for calculating straight line equations whichdetermine the initial sequence and the modified sequences,

[0014] —calculation means for calculating for the initial sequence andthe modified sequences a mean difference between the initial or modifiedphases and the phases produced by the corresponding straight lineequation, said final sequence being formed by the sequence whose meandifference is minimal.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] These and other aspects of the invention are apparent from andwill be elucidated, by way of non-limitative example, with reference tothe embodiment(s) described hereinafter.

[0016] In the drawings:

[0017] —FIG. 1 is a diagram of an example of a communication systemaccording to the invention,

[0018] —FIG. 2 is a flow chart describing the steps of a phaseestimation method,

[0019] —FIG. 3 is a flow chart diagram describing the operations used bythe phase jump correction and detection means according to theinvention,

[0020] —FIG. 4 is a representation of a phase sequence including a phasejump,

[0021] —FIG. 5 is a representation of a phase sequence including twophase jumps,

[0022] —FIG. 6 is a representation in the form of curves of the resultsobtained with the invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

[0023] In FIG. 1 is represented an example of a communication systemaccording to the invention. This communication system comprisesinteractive user terminals 1, which are transmitters within the meaningof the invention, and a head-end station 2, which is a receiver withinthe meaning of the invention. The head-end station 2 transmits signalsin a first frequency band Ku (12-14 GHz). These signals are relayed tointeractive user terminals 1 by a satellite 3. The interactive userterminals transmit signals in a second frequency band Ka (20-30 GHz).These signals are relayed to the head-end station 2 by the satellite 3.

[0024] Each terminal 1 comprises a data source 10 and channel codingmeans 12. The channel coding means deliver packets of N symbols whichcontain preamble symbols and data symbols. These packets are thentransmitted to filter means 13 and, finally, to modulation means 14,which use a local oscillator that has a frequency f_(c).

[0025] The head-end station 2 comprises demodulation means 20 which usea local oscillator that has a frequency f_(c)+Δf₀/Ts (where Δf₀ is anormalized frequency difference relative to the symbol frequency, and Tsis the duration of the symbols), and an initial phase Θ₀. The head-endstation 2 also comprises filter means 21 and sampling means 22, whichsample the output signal of the filter 21, to deliver symbols calledreceived symbols. The received symbols are transmitted to frequencyrecovery means 23 which estimate the normalized frequency difference Δf₀and correct the received symbols to compensate for the estimateddifference Δ̂  f₀.

[0026] The frequency recovery means 23 deliver frequency-correctedsymbols. These frequency-corrected symbols are transmitted to phaserecovery means 24. The phase-corrected and frequency-corrected symbolsare finally transmitted to channel decoding means 25 which deliver data27.

[0027] In the example described here, the phase recovery means 24comprise phase and frequency estimation means 50 and phase correctionmeans 51. The phase estimation means 50 are described with reference toFIG. 2. They are formed by a loop intended to be passed through L times.In the following of the description the index m (m=1 to L) is a loopcounter. Each value of m thus corresponds to one loop path. The loopcomprises:

[0028] —conventional phase estimation means 52 (for example, expectationmaximization) for producing an initial phase sequence S1 relating to asymbol packet r_(k) ^((m−1) (m=)1 to L, and k=1 to q, where q≦N),

[0029] —means 53 for calculating a frequency error relating to saidpacket, based on the initial sequence S1,

[0030] —means 54 for correcting the frequency of the symbols of thepacket, to correct said frequency error,

[0031] —loop means 55 which supply the frequency-corrected symbols r_(k)^((m)) to phase estimation means 52 for a following path through theloop,

[0032] —and loop output means 56 which supply to the phase correctionmeans 51 the phases estimated by the phase estimation means 52 (or,directly, the correction to be made), and the symbols to be corrected.

[0033] The calculation means 53 calculate a frequency error estimate{circumflex over (Δ)}f_(m) relating to the symbols r_(k) ^((M−1)) of asame packet, based on the initial phase sequence S1 produced by thephase estimation means 52. The values of this phase sequence S1 arebetween −∞ and +∞. The calculation means 53 comprise:

[0034] —means 60 for detecting and correcting phase jumps to correctthis initial sequence S1 and to deliver a final sequence S2,

[0035] —means 62 for calculating the slope of a straight line which isclosest possible to the values of the sequence S2, by applying theTretter algorithm. The slope obtained forms a frequency error estimate{circumflex over (Δ)}f_(m) relating to the symbols of the packet. It isthis frequency error that is transmitted to the frequency correctionmeans 54. The symbols obtained after frequency correction, r_(k)^((m))=r_(k) ^((m−1)).e^(−2πjk{circumflex over (Δ)}fm), are transmittedto the phase estimation means 52 for a new path through the loop. Duringthe last path through the loop (m=L), the symbols r_(k) ^((L−1))to becorrected and the phase correction ^(−jΘ̂_(k)^((L)))

[0036] to be made to these symbols are transmitted to the phasecorrection means 51.

[0037] The means 60 for detecting and correcting phase jumps arerepresented in FIG. 3. They comprise:

[0038] —means 100 for modifying the initial sequence to compensate for aplurality of phase jump configurations; the correction means 100 producea plurality of modified sequences which correspond each to thecorrection of a phase jump configuration;

[0039] —means 110 for calculating straight line equations whichdetermine the initial sequence and the modified sequences,

[0040] —calculation means 120 for calculating for the initial sequenceand the modified sequences a mean difference between the initial ormodified phases and the phases produced by the corresponding straightline equation, said final sequence being formed by the sequence whosemean difference is minimal.

[0041] The use of the means 60 for detecting and correcting phase jumpsis different and depends on the number of phase jumps one wishes tocorrect. But the method applied remains the same. The invention can thusbe applied to any number of phase jumps. Now two examples of embodimentwill be described of the means 60 for detecting and correcting phasejumps:

[0042] —a first example, in which the means 60 for detecting andcorrecting phase jumps are intended to correct a single phase jump of${\pm \frac{\pi}{2}};$

[0043] —a second example, in which the means 60 for detecting andcorrecting phase jumps are intended to correct two phase jumps of$\pm \frac{\pi}{2}$

[0044] in the same direction; this second example corresponds to themost probable case where the transmitted packets are ATM cells of 53octets.

[0045] In the examples that will be described, the modification means100 modify the initial sequence S1 phase by phase. But, for diminishingthe number of calculations to be performed, it is possible to modify thesequence phase-group by phase-group. This is equivalent to compensatingonly for certain configurations of phase jumps.

[0046] The first example of embodiment of the means 60 for detecting andcorrecting phase jumps is described with reference to FIG. 4. In FIG. 4is represented an example of an initial sequence S I comprising a phasejump of $+ {\frac{\pi}{2}.}$

[0047] The means 60 for detecting and correcting phase jumps have fortheir function to detect the position and the direction of the phasejump and then correct it. Therefore, as indicated in FIG. 3, theyperform the following operations:

[0048] a) The Tretter algorithm is applied to the initial sequence S1formed by phases (φ_(j)(j=0 to q−1) to obtain the straight line equationD₀ which determines this sequence. This equation is written as:D_(0: y=a) ₀.x+b₀ with:

a₀=α.S′−β.S and b₀ =γ.S−β.S′

[0049] where${S = {\sum\limits_{j = 0}^{q - 1}\quad \phi_{j}}},{S^{\prime} = {\sum\limits_{j = 0}^{q - 1}\quad {j \cdot \phi_{j}}}},{\alpha = {12/\left( {q \cdot \left( {q^{2} - 1} \right)} \right)}},{\beta = {6/\left( {q \cdot \left( {q + 1} \right)} \right)}}$

[0050] and

γ=2(2q -1)/(q(q +1))

[0051] These expressions can easily be derived from the calculationsshown on pages 523 and 524 of the title <<Numerical Recipes in C, theart of scientific computing, second edition>>by W. H. Press, S. A.Teukolsky, W. T. Vetterling, and B. P. Flannery, published by CambridgeUniversity Press in 1995, while considering that the uncertainty of thephases is constant whatever j.

[0052] b) An initial mean difference (σ₀)² is calculated between thephases φ_(j) of the initial sequence S1 and the phases y(j) coming fromthe straight line equation D₀.$\left( \sigma_{0} \right)^{2} = {\frac{1}{q}{\sum\limits_{j = 0}^{q - 1}\quad {{\phi_{j} - \left( {{a_{0} \cdot j} + b_{0}} \right)}}^{2}}}$

[0053] c) The initial sequence S1 is run through point by point bystarting from the end (symbol of rank q−1); the index i is a counterthat indicates the position of the phase jump (i=q−1, . . . , 0).

[0054] d) With each step the phases φj (j=q−i, . . . , q −1) aremodified by ${+ \frac{\pi}{2}},$

[0055] so that a modified sequence C_(i)+is obtained. This sequenceC_(i) ⁺is thus constituted by phases${\phi \quad}_{j}^{+} = \left\{ \begin{matrix}{{{\phi_{j}\quad {pour}\quad j} = 0},\ldots \quad,{q - i - 1}} \\{{{\phi_{j}\quad + {\frac{\pi}{2}\quad {pour}\quad j}} = {q - i}},\ldots \quad,{q - 1}}\end{matrix} \right.$

[0056] e) With each step one straight line equation D_(i) ⁺iscalculated, which straight lines determine the modified sequence C_(i)⁺. This equation is written as:D_(i)⁺ : y = (a_(i))⁺ ⋅ x + (b_(i))⁺  with:  a_(i)⁺ = α ⋅ (S_(i)^(′))⁺ − β ⋅ (S_(i))⁺  and  b_(i)⁺ = γ ⋅ (S_(i))⁺ − β ⋅ (S_(i)^(′))⁺  ${{where}\quad \left( S_{i} \right)^{+}} = {{\sum\limits_{j = 0}^{q - 1}\quad \phi_{j}^{+}} = {{S + {{i \cdot \frac{\pi}{2}}\quad {and}\quad \left( S_{i}^{\prime} \right)^{+}}} = {{\sum\limits_{j = 0}^{q - 1}\quad {j \cdot \phi_{j}^{+}}} = {S^{\prime} + {\frac{\pi}{2} \cdot {i\left( {q - \frac{\left( {i + 1} \right)}{2}} \right)}}}}}}$

[0057] that is to say,$a_{i}^{+} = {{a_{0} + {\alpha \cdot \frac{\pi}{2} \cdot i \cdot \left( {q - \frac{i + 1}{2}} \right)} - {\beta \cdot i \cdot \frac{\pi}{2}}} = {{a_{0} + {\left( A_{i}^{+} \right)\quad {with}\quad \left( A_{i}^{+} \right)}} = {{\alpha \cdot \frac{\pi}{2} \cdot i \cdot \left( {q - \frac{i + 1}{2}} \right)} - {\beta \cdot i \cdot \frac{\pi}{2}}}}}$${{and}\quad b_{i}^{+}} = {{b_{0} + {\gamma \cdot i \cdot \frac{\pi}{2}} - {\beta \cdot \frac{\pi}{2} \cdot i \cdot \left( {q - \frac{i + 1}{2}} \right)}} = {{b_{0} + {\left( B_{i}^{+} \right)\quad {with}\quad \left( B_{i}^{+} \right)}} = {{\gamma \cdot i \cdot \frac{\pi}{2}} - {\beta \cdot \frac{\pi}{2} \cdot i \cdot \left( {q - \frac{i + 1}{2}} \right)}}}}$

[0058] f) For each modified sequence C_(i) ⁺is calculated a meandifference (σ₁ ⁺) )2 between the phases φ_(j) ⁺of the modified sequenceC_(i) ⁺and the phases (yj) coming from the straight line equation D_(i)⁺.$\left( \sigma_{i}^{+} \right)^{2} = {\frac{1}{q}{\sum\limits_{j = 0}^{q - 1}\quad {{\phi_{j}^{+} - \left\lbrack {{\left( a_{i} \right)^{+} \cdot j} + \left( b_{i} \right)^{+}} \right\rbrack}}^{2}}}$

[0059] g) The operations c) to f) are repeated while the phasesφ_(j)(j=q−i, . . . , q−1) of the initial sequence of $- \frac{\pi}{2}$

[0060] are modified. For each value of i, another modified sequenceC_(i) ⁻is obtained. It is formed by the phases$\phi_{j}^{-} = \left\{ \begin{matrix}{{{\phi_{j}\quad {for}\quad j} = 0},\ldots \quad,{q - i - 1}} \\{{{\phi_{j} - {\frac{\pi}{2}\quad {for}\quad j}} = {q - i}},\ldots \quad,{q - 1}}\end{matrix} \right.$

[0061] h) The final sequence S2 is formed by the sequence whose meandifference is minimal.

[0062] For a less complex use, the mean differences (φ₁ ⁺)² arecalculated based on the initial mean difference (σ₀)². One obtains:$\left( \sigma_{i}^{+} \right)^{2} = {\sigma_{0}^{2} + {2\pi {\sum\limits_{j = {q - i}}^{q - 1}\quad \phi_{j}}} - {2 \cdot \left( B_{i}^{+} \right) \cdot S} - {2{\left( A_{i}^{+} \right) \cdot S^{\prime}}} + {b_{0}\left\lbrack {{\left( A_{i}^{+} \right) \cdot q \cdot \left( {q - 1} \right)} + {2 \cdot \left( B_{i}^{+} \right) \cdot q} - {\pi \cdot i}} \right\rbrack} + {a_{0}\left\lbrack {\frac{\left( A_{i}^{+} \right) \cdot q \cdot \left( {q - 1} \right) \cdot \left( {{2q} - 1} \right)}{3} + {\left( B_{i}^{+} \right) \cdot q \cdot \left( {q - 1} \right)} - {\frac{\pi}{2} \cdot i \cdot \left( {{2q} - i - 1} \right)}} \right\rbrack} + {q \cdot \left( B_{i}^{+} \right)^{2}} + {\left( A_{i}^{+} \right) \cdot \left( B_{i}^{+} \right) \cdot q \cdot \left( {q - 1} \right)} + \frac{\left( A_{i}^{+} \right)^{2} \cdot q \cdot \left( {q - 1} \right) \cdot \left( {{2q} - 1} \right)}{6} - {\frac{\pi}{2} \cdot \left( A_{i}^{+} \right) \cdot i \cdot \left( {{2q} - i - 1} \right)} - {\pi \cdot \left( B_{i}^{+} \right) \cdot i} + {\frac{\pi^{2}}{4} \cdot i}}$

[0063] The mean difference (σ_(i) ⁻)² is obtained by replacing in theexpression of ( σ_(i) ⁻)²: (Bi+) by - (Bi).

[0064] The second example of embodiment of the means 60 for detectingand correcting phase jumps is described with reference to FIG. 5. InFIG. 5 is shown an example of an initial sequence S1 comprising twophase jumps of $+ {\frac{\pi}{2}.}$

[0065] At step d) the phases are modified by $+ \frac{\pi}{2}$

[0066] for the p symbols from rank q-k-p to q-k-1, and by +π for the ksymbols from rank q-k to q (k varies between 1 and q and p variesbetween 1 and q-k).

[0067] The modified sequences obtained at step d) are thus written as:$\phi_{j}^{+} = \left\{ {{\begin{matrix}{{{\phi_{j}\quad {for}\quad j} = 0},\ldots \quad,{q - k - p - 1}} \\{{{\phi_{j} + {\frac{\pi}{2}\quad {for}\quad j}} = {q - k - p}},\ldots \quad,{q - k - 1}} \\{{{\phi_{j}\quad + {\pi \quad {for}\quad j}} = {q - k}},\ldots \quad,q}\end{matrix}\phi_{j}^{-}} = \left\{ \begin{matrix}{{{\phi_{j}\quad {for}\quad j} = 0},\ldots \quad,{q - k - p - 1}} \\{{{\phi_{j} - {\frac{\pi}{2}\quad {for}\quad j}} = {q - k - p}},\ldots \quad,{q - k - 1}} \\{{{\phi_{j}\quad - {\pi \quad {for}\quad j}} = {q - k}},\ldots \quad,q}\end{matrix} \right.} \right.$

[0068] And the straight line equations calculated in step e) are writtenas:D_(p, k)⁺ : y = (a_(p, k)⁺) ⋅ x + (b_(p, k)⁺)  with:  (a_(p, k))⁺ = α ⋅ (S_(p, k)^(′))⁺ − β ⋅ (S_(p, k))⁺  and  (b_(p, k))⁺ = γ ⋅ (S_(p, k))⁺ − β ⋅ (S_(p, k)^(′))⁺  ${{{where}\quad \left( S_{p,k} \right)^{+}} = {{\sum\limits_{j = 0}^{q - 1}\quad \phi_{j}^{+}} = {S + p}}}{{{\cdot \frac{\pi}{2}} + {{k \cdot \pi}\quad {{and}\quad \left( S_{p,k}^{\prime} \right)}^{+}}} = {{\sum\limits_{j = 0}^{q - 1}\quad {j \cdot \phi_{j}^{+}}} = {S^{\prime} + {\frac{\pi}{2} \cdot p \cdot \left( {q - k - \frac{p + 1}{2}} \right)} + {\pi \cdot k \cdot \left( {q - \frac{\left( {k + 1} \right)}{2}} \right)}}}}\quad$

[0069] that is to say,$a_{p,k}^{+} = {{a_{0} + {\alpha \left\lbrack {{\frac{\pi}{2} \cdot p \cdot \left( {q - k - \frac{p + 1}{2}} \right)} + {\pi \cdot k \cdot \left( {q - \frac{k + 1}{2}} \right)}} \right\rbrack} - {\beta \left\lbrack {{p\frac{\pi}{2}} + {k\quad \pi}} \right\rbrack}} = {a_{0} + \left( A_{p,k}^{+} \right)}}$${{{with}\quad \left( A_{p,k}^{+} \right)} = {{\alpha \left\lbrack {{\frac{\pi}{2} \cdot p \cdot \left( {q - k - \frac{p + 1}{2}} \right)} + {\pi \cdot k \cdot \left( {q - \frac{k + 1}{2}} \right)}} \right\rbrack} - {\beta \left\lbrack {{p\frac{\pi}{2}} + {k\quad \pi}} \right\rbrack}}}\quad$${{and}\quad b_{p,k}^{+}} = {{b_{0} + {\gamma \left\lbrack {{p\frac{\pi}{2}} + {k\quad \pi}} \right\rbrack} - {\beta \left\lbrack {{\frac{\pi}{2} \cdot p \cdot \left( {q - k - \frac{p + 1}{2}} \right)} + {\pi \cdot k \cdot \left( {q - \frac{k + 1}{2}} \right)}} \right\rbrack}} = {b_{0} + \left( B_{p,k}^{+} \right)}}$${{{with}\quad \left( B_{p,k}^{+} \right)} = {{\gamma \left\lbrack {{p\frac{\pi}{2}} + {k\quad \pi}} \right\rbrack} - {\beta \left\lbrack {{\frac{\pi}{2} \cdot p \cdot \left( {q - k - \frac{p + 1}{2}} \right)} + {\pi \cdot k \cdot \left( {q - \frac{k + 1}{2}} \right)}} \right\rbrack}}}\quad$

[0070] For a less complex implementation, the mean differences (σ_(p,k)⁺)² )2 are calculated based on the initial mean difference (σ₀)^(2 .)The following expression is obtained: $\begin{matrix}{\left( \sigma_{p,k}^{+} \right)^{2} = \quad {\sigma_{0}^{2} + {2\pi {\sum\limits_{j = {q - k}}^{q - 1}\phi_{j}}} + {\pi {\sum\limits_{j = {q - k - p}}^{q - k - 1}\phi_{j}}} - {2 \cdot \left( B_{p,k}^{+} \right) \cdot S} - {2{\left( A_{p,k}^{+} \right) \cdot S^{\prime}}} +}} \\{\quad {{b_{0}\left\lbrack {{\left( A_{p,k}^{+} \right) \cdot q \cdot \left( {q - 1} \right)} + {2 \cdot \left( B_{p,k}^{+} \right) \cdot q} - {\pi \left( {p + {2k}} \right)}} \right\rbrack} +}} \\{\quad {{a_{0}\left\lbrack \frac{\left( A_{p,k}^{+} \right) \cdot q \cdot \left( {q - 1} \right) \cdot \left( {{2q} - 1} \right)}{3} \right.} + {\left( B_{p,k}^{+} \right) \cdot q \cdot \left( {q - 1} \right)} - {\frac{\pi}{2} \cdot p \cdot}}} \\{\left. \quad {\left( {{2q} - {2k} - p - 1} \right) - {\pi \cdot k \cdot \left( {{2q} - k - 1} \right)}} \right\rbrack + {q \cdot \left( B_{p,k}^{+} \right)^{2}} +} \\{\quad {{\left( A_{p,k}^{+} \right) \cdot \left( B_{p,k}^{+} \right) \cdot q \cdot \left( {q - 1} \right)} + \frac{\left( A_{p,k}^{+} \right)^{2} \cdot q \cdot \left( {q - 1} \right) \cdot \left( {{2q} - 1} \right)}{6} -}} \\{\quad {{\frac{\pi}{2} \cdot \left( A_{p,k}^{+} \right) \cdot p \cdot \left( {{2q} - {2k} - p - 1} \right)} - {\pi \cdot \left( A_{p,k}^{+} \right) \cdot k \cdot}}} \\{\quad {\left( {{2q} - k - 1} \right) - {\pi \cdot \left( B_{p,k}^{+} \right) \cdot \left( {p + {2k}} \right)} + {\frac{\pi^{2}}{4} \cdot \left( {p + {4k}} \right)}}}\end{matrix}$

[0071] The mean difference (σ_(p,k) ⁻)² is derived from the expression(σ_(p,k) ⁺)² by replacing π by −π, (A_(p,k) ³⁰) by −(A_(p,k) ³¹ ) and(B_(p,k) ⁺) by −(B_(p,k) ³¹).

[0072] It is evident that the means that have just been described arecalculation means advantageously used in the form of a computer programintended to be executed by a microprocessor placed in the receiver.

[0073] In FIG. 6 are shown the results obtained thanks to the inventionin a system as described with reference to FIGS. 1 and 2. The curves ofFIG. 6 represent the packet error rate (PER) plotted against thesignal-to-noise ratio (SNR) in the following three cases:

[0074] —curve R3: when the phase jumps are not detected;

[0075] —curve R2: when the phase jumps are detected and corrected withthe method according to the invention;

[0076] —curve R1: for a Gaussian channel (no imperfection as regardseither phase or frequency).

[0077] These curves have been obtained via:

[0078] —a QPSK modulation,

[0079] —a random initial frequency error Δf₀ comprised between −1% and+1% of the symbol frequency,

[0080] —a random initial phase error θ₀ comprised between −π et+π,

[0081] —packets which comprise a known preamble of 48 symbols [a₁, . . ., a₄₈] and a payload part [a₄₉, . . . , a₅₉₂] of 544 symbols,

[0082] —a frequency recovery algorithm (utilized by the means 23), whichuses the packet preambles, and which is applied before the phaseestimation, so that the residual frequency error Δf₁ before the phaseestimation is lower than or equal to 0.3% of the symbol frequency,

[0083] —phase estimation means 50 which are formed by a loop which ispassed through L=2 times,

[0084] —on transmission, a Reed Solomon coding and a convolution codingwhich is punctured in 64 states.

[0085] The invention is not restricted to the embodiments that have justbeen described by way of example. More particularly, it relates to anytype of receiver that utilizes a frequency error correction device ofthe Tretter type and, upstream of this device, a phase estimation devicebased on decisions made on the received symbols.

[0086] Moreover, the number of phase jumps that may be detected andcorrected by applying this method is arbitrary. When the transmitteddata packets are longer, it is possible to have more than two phasejumps. In that case, in order not to complicate the calculations toomuch, one advantageously chooses to divide the data packets into smallerportiona so as to be in the same position again where one has a maximumof two phase jumps per packet portion. The method described above isthus applied to each portion of the packet. It provides the position andthe direction of the various phase jumps. The phases are then correctedby a multiple of $\frac{\pi}{2}$

[0087] as a function of the direction of the jumps and their number.Then, the Tretter algorithm is applied to this corrected sequence toobtain the final frequency estimate. In order to avoid a jump occurringbetween two portions of a packet, it is desirable to provide an overlapbetween the various portions of the same packet.

[0088] The method proposed is generally used for any MPSK modulation byconsidering phase jumps of +2π/M(instead of ±π/2 for a QPSK modulation).

Claims:
 1. A communication system comprising at least a transmitter (1)and a receiver (2) intended to receive symbols coming from a PSKmodulation, and comprising estimation means (62) for estimating afrequency error relating to a symbol based on a sequence of symbolphases, characterized in that said receiver comprises calculation means(52) for calculating a phase sequence, called initial sequence (S1),based on decisions made on symbols, and means for detecting andcorrecting phase jumps in this initial sequence, to supply a phasesequence, called final sequence (S2), to said frequency error estimationmeans (62).
 2. A communication system as claimed in claim 1,characterized in that said means for detecting and correcting phasejumps comprise: modifying means (100) for modifying said initialsequence (S1) so as to produce a plurality of modified sequences (C₁ ⁺;C_(i) ⁻; C_(p,k) ⁺; C_(p,k) ⁻), which each compensate for a phase jumpconfiguration, calculation means (110) for calculating straight lineequations which determine the initial sequence (D₀) and the modifiedsequences (D₁ ⁺; D_(i) ⁻; D_(p,k) ⁺; D_(p,k) ⁻) calculation means (120)for calculating for the initial sequence and the modified sequences amean difference between the initial or modified phases and the phasesproduced by the corresponding straight line equation (σ₀ ²;(σ_(i)⁺)²;(σ_(i) ⁻)²;(σ_(p,k) ⁺)²;(σ_(p,k) ⁻)²), said final sequence beingformed by the sequence whose mean difference is minimal.
 3. Acommunication system as claimed claim 2, characterized in that saidinitial sequence is modified phase-group by phase-group.
 4. A receiverintended to be used in a communication system as claimed in one of theclaims 1 or
 2. 5. A receiver as claimed in claim 4, characterized inthat said initial sequence is modified phase-group by phase-group.
 6. Amethod of estimating a frequency error relating to a received symbolcoming from a PSK modulation, based on a sequence of symbol phases,characterized in that the method comprises a calculation step ofcalculating a phase sequence, called initial sequence, based ondecisions made on symbols, and a step of detecting and correcting phasejumps in this initial sequence, to produce a phase sequence, calledfinal sequence, used for the estimation of a frequency error.
 7. Amethod of detecting and correcting phase jumps in an initial sequence ofsymbol phases coming from a PSK modulation, characterized in that itcomprises: a step (c, d) of modifying said initial sequence (S1) so asto produce a plurality of modified sequences which each compensate for aphase jump configuration, a step of calculating straight line equationswhich determine the initial sequence (a) and the modified sequences (e),a calculation step of calculating for the initial sequence (a) and themodified sequences (f) a mean difference between the initial or modifiedphases and the phases produced by the corresponding straight lineequation, said final sequence being formed by the sequence whose meandifference is minimal.
 8. A method of detecting and correcting phasejumps as claimed in claim 7, characterized in that said initial sequenceis modified phase-group by phase-group.
 9. A program comprisinginstructions for implementing the steps of a method of detecting andcorrecting phase jumps as claimed in claim 7 when said program isexecuted by a processor.
 10. A program comprising instructions forimplementing the steps of a method of estimating a frequency errorrelating to a received symbol, as claimed in claim 6, when said programis executed by a processor.